Analemma

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In astronomy, an analemma (pronounced /ˌænəˈlɛmə/, Greek for the pedestal of a sundial) is a curve representing the angular offset of a celestial body (usually the Sun) from its mean position on the celestial sphere as viewed from another celestial body relative to the viewing body's celestial equator. For instance, knowing that Earth's average solar day is almost exactly 24 hours, an analemma can be traced by plotting the position of the Sun as viewed from a fixed position on Earth at the same time every day for an entire year. The resulting curve resembles a figure of eight. This curve is commonly printed on globes, usually in the eastern Pacific Ocean, the only large tropical region with very little land. It is possible, though challenging, to photograph the analemma, by leaving the camera in a fixed position for an entire year and snapping images on 24-hour intervals (or some multiple thereof).

There are three parameters that affect the size and shape of the analemma: obliquity, eccentricity, and the angle between the apse line and the line of solstices. For an object with a perfectly circular orbit and no axial tilt, the Sun would always appear at the same point in the sky at the same time of day throughout the year and the analemma would be a dot. For an object with a circular orbit but significant axial tilt, the analemma would be a figure of eight with northern and southern lobes equal in size. For an object with an eccentric orbit but no axial tilt, the analemma would be a straight east-west line along the equator.

The north-south component of the analemma is the declination, or the latitude at which the sun is directly overhead. The east-west component is the equation of time, or the difference between solar time and local mean time. This can be interpreted as how "fast" or "slow" the sun is compared to clock time.

An analemma that includes an image of a total solar eclipse is called a tutulemma — a term coined by photographers based on the Turkish word for eclipse.[1]

Contents

Earth's analemma

Owing to the tilt of Earth's axis (23.439°) and its elliptical orbit around the Sun, the relative location of the sun above the horizon is not constant from day to day when observed at the same clock time each day. Depending on one's geographical latitude, this loop will be inclined at different angles.

The figure on the left is an example of an Earth analemma as seen from the northern hemisphere. It is a plot of the position of the sun at 12:00 noon at Royal Observatory, Greenwich, England (latitude 51.4791°N, longitude 0°) during the year 2006. The horizontal axis is the azimuth angle in degrees (180° is facing south). The vertical axis is the altitude in degrees above the horizon. The first day of each month is shown in black, and the solstices and equinoxes are shown in green. It can be seen that the equinoxes occur at altitude φ = 90° − 51.4791° = 38.5209°, and the solstices occur at altitudes φ ± ε where ε is the axial tilt of the earth, 23.439°. The analemma is plotted with its width highly exaggerated, which permits noting that it is slightly asymmetrical (due to the two-week misalignment between the apsides of the Earth's orbit and its solstices).

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